What is the probability of someone out of 12 people know someone in a group of 41000?

Question

I live in a county of 41000 people. We have a grand jury of 12 people. I'm trying to figure out the chance of someone on the grand jury knowing someone who has been indicted.

Answer 1

Hi Elizabeth T.,

There's significant data missing from your question. Assuming that all individuals on the grand jury are residents of the county, and that the indicted person is also a resident of the county, you would still need to know the average number of "persons known" by an average person. Lets's say the average person knows (well enough to qualify for your question) 20 people. Then 12 jurors collectively know about 240 people in all, and the odds of any one of them knowing that particular indicted individual would be about 240/41000, or about 1 in 170. There are slight modifications to avoid overlapping people knowing, etc. but that's an insignificant possibility at such low odds.

Now, all of this assumes that grand juror pool selection is random among the county population (obviously, only adults, and probably those registered to vote, etc. actually count), and that the indicted person is also a randomly selected person. If there is residence-locational, socioeconomic, career or place-of-employment, religious, social-media, or any other type of connection between the jurors and the indicted person, those odds may certainly shift!

-- Cheers, -- Mr. d.